As far as I know there isn't one specified. As people craft badges booster packs are handed out.
You can influence the drop rate by rising your steam level. Every 10 levels you gain increase the drop chance by 20% (source).
How can I get a booster pack?
Once you have received all of your card drops, you become eligible for a booster pack, which is a set of 3 trading cards that may include both basic and foil cards. Booster packs are granted randomly to eligible users as more badges are crafted by members of the community. Make sure you log in to Steam each week to maintain eligibility.
Once eligible, your Steam Level increases your rate of receiving a booster pack drop:
Level 10: +20% increase in your drop rate
Level 20: +40% increase in your drop rate
Level 30: +60% increase in your drop rate
Level 40: +80% increase in your drop rate
Level 50: +100% increase in your drop rate (i.e. the rate has doubled)